(a) Fit a linear regression model using all 20 observations. What are the values of a, b, r2, and se? (Round your answers to three decimal places.) a=b=r2=se= (b) Fit a linear regression model with the two observations identified by arrows omitted. What are the values of a, b, r2, and se? (Round your answers to three decimal places.) a= b= r2= se= (c) In a few sentences, describe any differences you found in parts (a) and (b). The y-intercept (increased/decreased/stayed the same) .The slope (increased/decreased/stayed the same) .The value of r2 (increased/decreased/stayed the same) .The value of se (increased/decreased/stayed the same). (d) The researchers could use the estimated regression equation based on all 20 observations to make predictions for latitudes ranging from 58 to 64, or they could use the estimated regression equation based on the 18 observations (omitting the two observations identified by arrows) to make predictions for latitudes ranging from 58 to 61. Which strategy would you recommend, and why? A) One would expect more accurate predictions from the line using 20 observations due to the decreased r2 value and increased se. B) One would expect more accurate predictions from the line using 18 observations due to the decreased r2 value and increased se. C) The two lines would provide equally accurate predictions. D) One would expect more accurate predictions from the line using 20 observations due to the increased r2 value and decreased se. E) One would expect more accurate predictions from the line using 18 observations due to the increased r2 value and decreased se.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
15.3 #5
- (58.7, 46)
- (58.2, 35.9)
- (58.2, 34.8)
- (59.4, 32.3)
- (60, 32.9)
- (59.4, 29.7)
- (60.8, 26.3)
- (60.9, 26.8)
- (63.4, 28.8)
- (63.4, 19.2)
- (59.1, 27)
- (59.3, 26.2)
- (59.5, 25.7)
- (59.5, 27.6)
- (59.7, 19.2)
- (59.8, 24.4)
- (60.5, 22.4)
- (60.7, 17.9)
- (60.7, 13)
- (61.1, 11.8)
Flowering Range Versus Latitude: Anemone Hepatica
Latitude (N) | Flowering Date Range |
---|---|
58.7 | 46.0 |
58.2 | 35.9 |
58.2 | 34.8 |
59.4 | 32.3 |
60.0 | 32.9 |
59.4 | 29.7 |
59.1 | 27.0 |
59.3 | 26.2 |
59.5 | 25.7 |
59.5 | 27.6 |
59.7 | 19.2 |
59.8 | 24.4 |
60.8 | 26.3 |
60.9 | 26.8 |
63.4 | 28.8 |
63.4 | 19.2 |
60.5 | 22.4 |
60.7 | 17.9 |
60.7 | 13.0 |
61.1 | 11.8 |
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